Abstract

In this thesis, we present Kohn variational calculations of scattering and annihilation parameters for very low energy interactions of positrons with molecular hydrogen. Our analysis includes the first application of the Kohn method for this system in which the interelectronic potential in the molecular target is treated explicitly. All previous Kohn calculations on positron hydrogen molecule scattering have avoided this complication by the use of the method of models. The advantage of the explicit treatment over the method of models is that it allows approximate target wavefunctions of a very high accuracy to be admitted more easily to the Kohn calculations. We find that the accuracy of the approximate target wavefunction is an extremely important factor in obtaining reliable results from the calculations.

We carry out an extensive investigation of anomalous, nonphysical behaviour in the results of our Kohn calculations. Our explanations of how these anomalies arise and how they may be avoided significantly improves upon the discussions of these phenomena given in earlier accounts of positron hydrogen molecule scattering calculations by other authors.

As with all previous models of positron hydrogen molecule scattering, we find discrepancies between the experimental value of the annihilation parameter, Z effective, and the theoretical value of this quantity as determined from our Kohn calculations. Limitations of the model that could explain these discrepancies are discussed and suggestions for future improvements are proposed.